293 citations · 1.2k across the 39 of their papers we have counts for
39 papers
High-order accurate structure-preserving finite volume schemes on adaptive moving meshes for shallow water equations: Well-balancedness and positivity
Zhihao Zhang, Huazhong Tang, Kailiang Wu
This paper develops high-order accurate, well-balanced (WB), and positivity-preserving (PP) finite volume schemes for shallow water equations on adaptive moving structured meshes.…
High-order accurate positivity-preserving and well-balanced discontinuous Galerkin schemes for ten-moment Gaussian closure equations with source terms
Jiangfu Wang, Huazhong Tang, Kailiang Wu
This paper proposes novel high-order accurate discontinuous Galerkin (DG) schemes for the one- and two-dimensional ten-moment Gaussian closure equations with source terms defined b…
A new discretely divergence-free positivity-preserving high-order finite volume method for ideal MHD equations
Shengrong Ding, Kailiang Wu
This paper proposes and analyzes a novel efficient high-order finite volume method for the ideal magnetohydrodynamics (MHD). As a distinctive feature, the method simultaneously pre…
Provably convergent Newton-Raphson methods for recovering primitive variables with applications to physical-constraint-preserving Hermite WENO schemes for relativistic hydrodynamics
Chaoyi Cai, Jianxian Qiu, Kailiang Wu
The relativistic hydrodynamics (RHD) equations have three crucial intrinsic physical constraints on the primitive variables: positivity of pressure and density, and subluminal flui…
Critical Sampling for Robust Evolution Operator Learning of Unknown Dynamical Systems
Ce Zhang, Kailiang Wu, Zhihai He
Given an unknown dynamical system, what is the minimum number of samples needed for effective learning of its governing laws and accurate prediction of its future evolution behavio…
Deep-OSG: Deep Learning of Operators in Semigroup
Junfeng Chen, Kailiang Wu
This paper proposes a novel deep learning approach for learning operators in semigroup, with applications to modeling unknown autonomous dynamical systems using time series data co…
On Optimal Cell Average Decomposition for High-Order Bound-Preserving Schemes of Hyperbolic Conservation Laws
Shumo Cui, Shengrong Ding, Kailiang Wu
This paper presents the first systematic study on the fundamental problem of seeking optimal cell average decomposition (OCAD), which arises from constructing efficient high-order…
A New Locally Divergence-Free Path-Conservative Central-Upwind Scheme for Ideal and Shallow Water Magnetohydrodynamics
Alina Chertock, Alexander Kurganov, Michael Redle +1
We develop a new second-order unstaggered path-conservative central-upwind (PCCU) scheme for ideal and shallow water magnetohydrodynamics (MHD) equations. The new scheme possesses…
High order asymptotic preserving finite difference WENO schemes with constrained transport for MHD equations in all sonic Mach numbers
Wei Chen, Kailiang Wu, Tao Xiong
In this paper, a high-order semi-implicit (SI) asymptotic preserving (AP) and divergence-free finite difference weighted essentially nonoscillatory (WENO) scheme is proposed for ma…
Positivity-Preserving Well-Balanced Central Discontinuous Galerkin Schemes for the Euler Equations under Gravitational Fields
Haili Jiang, Huazhong Tang, Kailiang Wu
This paper designs and analyzes positivity-preserving well-balanced (WB) central discontinuous Galerkin (CDG) schemes for the Euler equations with gravity. A distinctive feature of…
A Physical-Constraint-Preserving Finite Volume WENO Method for Special Relativistic Hydrodynamics on Unstructured Meshes
Yaping Chen, Kailiang Wu
This paper presents a highly robust third-order accurate finite volume weighted essentially non-oscillatory (WENO) method for special relativistic hydrodynamics on unstructured tri…
Is the Classic Convex Decomposition Optimal for Bound-Preserving Schemes in Multiple Dimensions?
Shumo Cui, Shengrong Ding, Kailiang Wu
Since proposed in [X. Zhang and C.-W. Shu, J. Comput. Phys., 229: 3091--3120, 2010], the Zhang--Shu framework has attracted extensive attention and motivated many bound-preserving…
Provably Positive Central DG Schemes via Geometric Quasilinearization for Ideal MHD Equations
Kailiang Wu, Haili Jiang, Chi-Wang Shu
In the numerical simulation of ideal MHD, keeping the pressure and density positive is essential for both physical considerations and numerical stability. This is a challenge, due…
On Energy Laws and Stability of Runge--Kutta Methods for Linear Seminegative Problems
Zheng Sun, Yuanzhe Wei, Kailiang Wu
This paper presents a systematic theoretical framework to derive the energy identities of general implicit and explicit Runge--Kutta (RK) methods for linear seminegative systems. I…
Geometric Quasilinearization Framework for Analysis and Design of Bound-Preserving Schemes
Kailiang Wu, Chi-Wang Shu
Solutions to many partial differential equations satisfy certain bounds or constraints. For example, the density and pressure are positive for equations of fluid dynamics, and in t…
Deep Neural Network Modeling of Unknown Partial Differential Equations in Nodal Space
Zhen Chen, Victor Churchill, Kailiang Wu +1
We present a numerical framework for deep neural network (DNN) modeling of unknown time-dependent partial differential equations (PDE) using their trajectory data. Unlike the recen…
Minimum Principle on Specific Entropy and High-Order Accurate Invariant Region Preserving Numerical Methods for Relativistic Hydrodynamics
Kailiang Wu
This paper explores Tadmor's minimum entropy principle for the relativistic hydrodynamics (RHD) equations and incorporates this principle into the design of robust high-order disco…
Uniformly High-Order Structure-Preserving Discontinuous Galerkin Methods for Euler Equations with Gravitation: Positivity and Well-Balancedness
Kailiang Wu, Yulong Xing
This paper presents a class of novel high-order accurate discontinuous Galerkin (DG) schemes for the compressible Euler equations under gravitational fields. A notable feature of t…
Methods to Recover Unknown Processes in Partial Differential Equations Using Data
Zhen Chen, Kailiang Wu, Dongbin Xiu
We study the problem of identifying unknown processes embedded in time-dependent partial differential equation (PDE) using observational data, with an application to advection-diff…
A Non-Intrusive Correction Algorithm for Classification Problems with Corrupted Data
Jun Hou, Tong Qin, Kailiang Wu +1
A novel correction algorithm is proposed for multi-class classification problems with corrupted training data. The algorithm is non-intrusive, in the sense that it post-processes a…
Provably Physical-Constraint-Preserving Discontinuous Galerkin Methods for Multidimensional Relativistic MHD Equations
Kailiang Wu, Chi-Wang Shu
We propose and analyze a class of robust, uniformly high-order accurate discontinuous Galerkin (DG) schemes for multidimensional relativistic magnetohydrodynamics (RMHD) on general…
Data-Driven Deep Learning of Partial Differential Equations in Modal Space
Kailiang Wu, Dongbin Xiu
We present a framework for recovering/approximating unknown time-dependent partial differential equation (PDE) using its solution data. Instead of identifying the terms in the unde…
Entropy Symmetrization and High-Order Accurate Entropy Stable Numerical Schemes for Relativistic MHD Equations
Kailiang Wu, Chi-Wang Shu
This paper presents entropy symmetrization and high-order accurate entropy stable schemes for the relativistic magnetohydrodynamic (RMHD) equations. It is shown that the conservati…
Structure-preserving Method for Reconstructing Unknown Hamiltonian Systems from Trajectory Data
Kailiang Wu, Tong Qin, Dongbin Xiu
We present a numerical approach for approximating unknown Hamiltonian systems using observation data. A distinct feature of the proposed method is that it is structure-preserving,…